English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider two natural problems arising in geometry which are equivalent tothe local solvability of specific equations of Monge-Ampere type. These twoproblems are: the local isometric embedding problem for two-dimensionalRiemannian manifolds, and the problem of locally prescribed Gaussian curvaturefor surfaces in R^3. We prove a general local existence result for a largeclass of Monge-Ampere equations in the plane, and obtain as corollaries theexistence of regular solutions to both problems, in the case that the Gaussiancurvature vanishes to arbitrary finite order on a single smooth curve.

The Local Isometric Embedding in R^3 of Two-Dimensional Riemannian Manifolds With Gaussian Curvature Changing Sign to Finite Order on a Curve